Jonas Gahr Støre, leader of the opposition Labour Party, gained parliamentary majority support for the motion, which will see a vote on a rule change which would block Hagen from being elected to the committee.
Støre's proposal is a response to Hagen, and influential former leader of the populist Progress Party, being nominated by that party as its representative on the committee, which awards the Nobel Peace Prize.
In accordance with Alfred Nobel's (1833-1896) will, the Norwegian parliament is responsible for appointing the Nobel Committee's members, but its choices must reflect a political balance of power.
As the country's third-largest party in the September legislative elections, the Progress Party is entitled to choose a member for the committee.
Critics fear that Hagen, currently a deputy MP with the party, could jeopardise the committee's reputation as an independent body.
Although the move to expedite the vote by Støre is rare in Norwegian politics, the Labour leader was supported by both right-centre and left-centre parties in the proposal.
Bringing the vote forward means that any new rules will be in place before parliament nominates its final members to the committee.
The new rule would block Hagen's nomination on the grounds that he is currently a deputy MP.
Although rules prevent currently-serving MPs from sitting on the Nobel Committee, it is unclear whether these also apply to deputy members.
Government coalition partners the Conservatives and Progress opposed the expedited vote as well as moves to prevent Hagen from joining the committee.
“It would be very bad, very bad if a majority was established in parliament which in reality would keep Carl I. Hagen off the Nobel Committee. We must have respect for each other's candidates,” Progress parliamentary leader Hans Andreas Limi told newspaper VG on Friday.
Støre told VG that the proposal was not about Carl I. Hagen, but about whether deputy parliamentary representatives should be allowed to sit on the Nobel Committee.
In addition to his current role as an elected official, Hagen is also a controversial choice due to his contentious personality.
He once claimed that "a society without ethnic minorities is a society in harmony".
The former secretary of the Nobel Committee, Geir Lundestad, told broadcaster NRK last month that Hagen is "particularly inadequate" for the job.